There are three consecutive integers such that twice the sum of the smallest and the largest is eight more than twice the largest. Find the smallest integer in the sequence.

Question

asked Apr 24, 2021 213k views

1 Answer

Jeremy Meadows · Answer 1 · 2021-04-30T11:22:15+0000

Answer: 4

Explanation:

Let the consecutive integers be x, x+1 and x+2.

There are three consecutive integers such that twice the sum of the smallest and the largest is eight more than twice the largest. This means that:

2(x + x+2) = 2(x+2) + 8

2(2x + 2) = 2x + 4 + 8

4x + 4 = 2x + 12

Collect like terms

4x - 2x = 12 - 4

2x = 8

x = 8/2

x = 4

The smallest integer in the sequence is 4